My question: since neoclassical economics atomizes the representative agent, wouldn’t a modern theory without hardcore math be like a particle physics in English? There are a few posts about the (over) use of abstruse math in economics. I don’t want to comment too much: this conversation is well above my intellectual pay grade. I have a hard time getting through an economics paper (sometimes I manage, and I do actually try to go through the whole paper). I’m pretty good at math. Just not *that* good. (Disclaimer: I’m writing this for my own benefit, and have no deep understanding in this part of economics).

I sympathize both with both sides, and I think Paul Krugman is right in emphasizing math as a way of preventing sloppy thinking. This is especially true for a subject like economics where there are only relative, not absolute, microfoundations. Economists get to choose what’s endogenous and what is not in a way that illuminates a particular point. Caplan’s says math doesn’t reveal anything that’s not already obvious. That’s because economists, unlike any other scientists, create their own world. If I assume a world without gravity, than I won’t be surprised to mathematically prove my ability to fly.

Economics jumps several logical levels in its use of math. Normally, in a reductionist framework, the farther you get away from small microfoundations, the less mathematical a subject becomes. It is possible, a hypothetically extreme reductionist might say, to reduce macroeconomics to microeconomics to psychology to neurobiology to biochemistry to physical chemistry to atomic physics to quantum physics. As the level of abstraction increases, the use of math falls – to the point where psychologists use math almost solely for empirical examination. But economics is an outlier: the principal charge of neoclassical econ is *atomizing the individual*. But in doing so, we loose the foundations from “lower” disciplines, and hence must assume our own. Economists, in other words, may create the world.

In that sense, asking a neoclassical to get beyond the math is like asking a physicist to talk in English. Bryan Caplan – who genuinely believes in modern insights – cannot ignore the math any more than he can abandon the “neo” in “neoclassical”.

Math is important for the same reason it (can be) useless. Since economics starts from scratch in a way no other science other than physics does, math tells us *precisely* what assumptions are made to reach a certain conclusion. Normally we think assumptions first, conclusion later, but let’s say I make a statement like:

Deficit spending can never be expansionary.

By itself, this means nothing. It might be an axiom for all I know. But let’s say it’s not, and we’re talking about a model with representative, rational agents. With math, you can “fill in” all the “holes” (find all necessary assumptions) to reach this conclusion. In that sense, it helps us backward engineer what a model specifically dictates.

You know this conclusion is true when we consider immortal agents which maximize intertemporal consumption. And given a more complex setup, there are many ways in which this particular conclusion may be reached.

You can explain this in English *after the fact*. This is slightly different from Paul Krugman’s point, which is working from the assumptions to a conclusion. The importance of math comes in seeing *all the assumptions* necessary for a conclusion. I don’t see how English does this. It’s not all about *explanation*.

Perhaps my confusion is reconciling Caplan’s comments on math with his comments on neoclassical economics:

Here are a few of the best new ideas to come out of academic economics since 1949:

- Human capital theory
- Rational expectations macroeconomics
- The random walk view of financial markets
- Signaling models
- Public choice theory
- Natural rate models of unemployment
- Time consistency
- The Prisoners’ Dilemma, coordination games, and hawk-dove games
- The Ricardian equivalence argument for debt-neutrality
- Contestable markets

This can all easily be explained in English. But in the process of reaching a conclusion, we can trip over our own English, *unless the world has no frictions*. But once it does, math is like a gutter rail to crazy thinking.

In some ways, mathematics *philosophically* echoes rational agent economics itself: there are many ways one can be irrational (or wrong), but only one in which he can be rational (or right).

Caplan the blogger or teacher can be aghast with some of the math he sees. But Caplan the neoclassical surely agrees that an economics without math would be like physics written in Iambic Pentameter?

P.S. Caplan challenges Krugman to identify a subject in economics where the insights cannot be explained in English to someone not brainwashed by math-econ. I wonder if he can describe to me a full, neoclassical model with all the *best things* about modern economics, without any complicated math. I would be grateful, since I’m not good enough to understand some of the papers I’d like too.